Abstract
A bounded operator S on a Hilbert space is hyponormal if S∗S −SS∗ is positive. In this work we find necessary conditions for the hyponormality of the Toeplitz operator Tf+g on the Bergman space of the annulus {1/2 < |z| < 1}, where f and g are analytic and f satisfies a smoothness condition.
Highlights
A bounded operator S on a Hilbert space is hyponormal if S∗S − SS∗ is positive
Hyponormality of Toeplitz operators has been studied by many authors
Toeplitz operators on A21/2 are defined by Tf (h) = P, where f is bounded and measurable on C1/2, P is the orthogonal projection on
Summary
Hyponormality of Toeplitz operators has been studied by many authors. Hyponormality of these operators on the Hardy space was considered in [3, 4]. An improvement of the necessary condition in the case when g1 and g2 are binomials is given in [5]. In this work we consider hyponormality of Toeplitz operators on the Bergman space of an annulus. Toeplitz operators on A21/2 are defined by Tf (h) = P (hf ), where f is bounded and measurable on C1/2, P is the orthogonal projection on. Toeplitz operator; Bergman space of an annulus; hyponormal; positive matrix. We consider hyponormality of Toeplitz operators with a symbol of the form f = g1 + g2, where g1 and g2 are bounded analytic functions on C1/2. We begin by recalling some known properties of Toeplitz operators
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